Question: $g(x) = -3x^{2}-6x-4(f(x))$ $f(t) = -t-2$ $ f(g(-8)) = {?} $
Answer: First, let's solve for the value of the inner function, $g(-8)$ . Then we'll know what to plug into the outer function. $g(-8) = -3(-8)^{2}+(-6)(-8)-4(f(-8))$ To solve for the value of $g$ , we need to solve for the value of $f(-8)$ $f(-8) = -(-8)-2$ $f(-8) = 6$ That means $g(-8) = -3(-8)^{2}+(-6)(-8)+(-4)(6)$ $g(-8) = -168$ Now we know that $g(-8) = -168$ . Let's solve for $f(g(-8))$ , which is $f(-168)$ $f(-168) = -(-168)-2$ $f(-168) = 166$